As a ramification of a motivational discussion for previous joint work, in which equations of motion for the finite spectral action of the standard model were derived, we provide a new analysis of the results of the calculations therein, switching from the perspective of spectral triple to that of Fredholm module and thus from the analogy with Riemannian geometry to the premetrical structure of the noncommutative geometry. Using a suggested noncommutative version of Morse theory together with algebraic theory to analyze the vacuum solutions, the first two summands of the algebra for the finite triple of the standard model arise up to Morita equivalence. We also demonstrate a new vacuum solution whose features are compatible with the physical mass matrix.
Skip Nav Destination
Article navigation
November 2006
Research Article|
November 22 2006
Noncommutative geometry, topology, and the standard model vacuum
R. A. Dawe Martins
R. A. Dawe Martins
a)
Nottingham University
, University Park, Nottingham NG7 2RD, United Kingdom
Search for other works by this author on:
a)
Present address: Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal; electronic mail: [email protected]
J. Math. Phys. 47, 113507 (2006)
Article history
Received:
January 02 2006
Accepted:
October 04 2006
Citation
R. A. Dawe Martins; Noncommutative geometry, topology, and the standard model vacuum. J. Math. Phys. 1 November 2006; 47 (11): 113507. https://doi.org/10.1063/1.2374880
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Related Content
Morita equivalence of noncommutative supertori
J. Math. Phys. (June 2010)
Gauge transformations of spectral triples with twisted real structures
J. Math. Phys. (August 2021)
On the scalar curvature for the noncommutative four torus
J. Math. Phys. (June 2015)
Noncommutative model with spontaneous time generation and Planckian bound
J. Math. Phys. (October 2005)
Massive neutrinos in almost-commutative geometry
J. Math. Phys. (February 2007)